If you lowered 10 m^3 of sand (61kWh of potential energy), to generate the minimum 100kW power to participate in grid stabilization markets, you'd have to drop that 16000kg of sand for 61kWh/100kW = 0.61hr = 2196 sec. 1400 meters in 2196 seconds is 0.64 m/sec. That seems reasonable, but you'd need a lot of these (so a wide mineshaft) to generate a more meaningful amount of power (like at least 1 MW). Current grid scale batteries are capable of outputting hundreds of MW of power.
https://en.wikipedia.org/wiki/Battery_storage_power_station
> we can store 3000m^3 of sand, so that's 18MWh.
> I'm sure they've got a lot more space than that, but it just gives some idea of how much sand you're talking about.
They're going to need 3 orders of magnitude more space then because current generation grid scale batteries store GWh of energy, and generally speaking lower cost energy storage competes by offering much higher storage capacity.
However, having the lower minimum has the advantage of allowing smaller firms to participate (i.e. companies controlling 100s of electric water heaters), instead of just massive utilities.
It's always going to be easier to move water around in an automated fashion, though, so I'm immediately skeptical of any system that isn't some variant of two tanks and a pump/turbine.
If you really do want to use gravity as a power source and don't want to go the hydro route you're better off building narrow-gauge train lines up the sides of hills. The lower-impact and lower-output version of that would be aerial ropeways.
A machine for lifting/lowering loose material is more complicated than a pump, no doubt about that. But a deep shaft would mean that you don't build one machine per shaft, you build a few dozen smaller ones with a good handover mechanism and start getting small serial production benefits right from the first installation. Capacity would be virtually infinite, because with excess energy you could just mine more of whatever stuff is down there.
I guess if it's expensive to switch the dry mass mechanism between directions or speed states, it might be worthwhile to prepare some basin volume up and down and run a small capacity pumped storage in parallel at the same site for higher frequency load changes and short peaks. You might even find yourself discharging the wet battery while charging the dry one or the reverse if there is a sufficient delta in dispatchability.
Potential energy, U = mgh. So the energy required to raise 1m^3 of sand 1400m is 1600 x 1400 x 9.8 = 22MJ = 6.1kWh
I've no idea how large their mine galleries are, but lets say they're 3m wide x 2m high - in 500m of gallery, we can store 3000m^3 of sand, so that's 18MWh.
I'm sure they've got a lot more space than that, but it just gives some idea of how much sand you're talking about.